check out the superfractalthing threads, there is lots of discussion of such things, including knighty's method which uses interval arithmetic to compute the truncation error on the series
Could you point me to the post by knighty which explains the interval arithmetic method? I found two superfractalthing threads that are several pages long so it takes some time to go through all of the posts.
After reading some of the posts I see that the "perfect" way of computing how many iterations can be skipped via SA is to:
1. Compute the iterations for each pixel using the normal perturbation method without SA.
2. For each pixel go through the iterations, starting at 0, and compare the value calculated by the SA formula to the value calculated by the perturbation method.
3. Once the difference between the values exceeds some preset value, then all the previous iterations can be skipped via SA.
Obviously this method won't improve performance compared to regular perturbation without SA because you are calculating the full image using normal perturbation anyway. One way to make it practical is to only perform this check on the four pixels at the corners of the image, and use the lowest amount of iterations that can be skipped among the four pixels for the whole image.
September 17, 2010, 05:46:53 AM
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